SOLUTION: A (0,1) , B (-2,3) , C (2,-1) are the vertices of a triangle ABC. P and Q are the midpoints of the sides AB and AC. Show that PQ is parallel to BC.

Algebra ->  Linear-equations -> SOLUTION: A (0,1) , B (-2,3) , C (2,-1) are the vertices of a triangle ABC. P and Q are the midpoints of the sides AB and AC. Show that PQ is parallel to BC.      Log On


   

Question 856883: A (0,1) , B (-2,3) , C (2,-1) are the vertices of a triangle ABC. P and Q are the midpoints of the sides AB and AC.
Show that PQ is parallel to BC.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
P: x=%280-2%29%2F2=-1; y=%281%2B3%29%2F2=2
P is (-1,2)
-
Q: x=%280%2B2%29%2F2=1; y=%281-1%29%2F2=0
Q is (1,0)
-
Slope of BC, %283-%28-1%29%29%2F%28-2-2%29=4%2F%28-4%29=-1.
Slope of PQ, %282-0%29%2F%28-1-1%29=2%2F%28-2%29=-1.
Slopes of BC and PQ are both -1, equal, so BC and PQ are parallel.